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Stochastic homogenization of quasilinear PDEs with a spatial degeneracy. (English) Zbl 1180.35591
This paper is devoted to the study of the stochastic homogenization for some degenerate quasilinear parabolic PDEs. The underlying nonlinear operator degenerates along the space variable, uniformly in the nonlinear term: the degeneracy points correspond to the degeneracy points of a reference diffusion operator on the random medium. Assuming that this reference diffusion operator is ergodic, the authors prove the homogenization property for the quasilinear PDEs, by means of the first-order approximation method. The (nonlinear) limit operator need not to be nondegenerate. Concrete examples are provided.

MSC:
35R60 PDEs with randomness, stochastic partial differential equations
35K65 Degenerate parabolic equations
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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